Tomographic processing method with a small number of projections of a contrasted object

ABSTRACT

A method for processing a sequence of a plurality of projection images of an object of interest is provided. The method, being recursive, comprises defining, a priori, a sparse image and a series of models for breaking down the object as a sum of a sparse component and of a complementary non-sparse component; initializing a sparse image depending on the sparse image defined a priori and initializing the series of models for breaking down the object; reconstructing an image of the sparse component of the decomposition model of the object from acquired projection images and from the initialized sparse image; and updating the sparse image so that, during the iterations, the reconstruction of the image of the sparse component gradually reintroduces the complementary component into the sparse image, in order to obtain a complete image of the non-sparse object.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Embodiments of the invention relate generally to tomographicreconstruction of an object and, more particularly, to medical imagingby tomographic reconstruction or tomosynthesis with a small number ofprojections (“few view tomography”).

2. Description of Related Art

The acquisition of 1D or 2D projection images of an object and thetomographic reconstruction of an image having a greater dimension,either 2D or 3D, of this object are schematically illustrated in FIG. 1.

The reconstruction of an image by tomography consists of emitting X-rays10 from a source towards the object 12, the X-rays are emitted accordingto different angulations l ∈ {1, . . . , L} which define the trajectoryTr of the source (commonly a rotation, also called “spin”). The 3Dreconstruction of the object is described below.

After having crossed the object 12, the X-rays are detected by adetector 13 so as to form a set of 2D projections. There are as manyacquired 2D projections as there are relevant angulations (i.e. Lprojections for the trajectory). The acquisition is applied by adetector 13 located facing the X-ray source 11, for example, a digitalcamera. It is possible to apply the acquisition with a fixed detectorand a source, which is not necessarily positioned facing the source.

An application of tomography is the detection and characterization of alesion in an organ, for example, a breast cancer tumour or stenosis in avessel of a patient. The acquired 2D projections are used forreconstructing a 3D image of the object. This 3D object is morespecifically a 3D mapping of X-ray attenuation coefficients of thecrossed medium. It is by means of this mapping that the radiologypractitioner interprets this image according to the observed contrastdifferences.

The commonly reconstructed 3D images (for example by an algorithm of thefiltered back-projection family) are affected with striations (streaks)due to the finite sampling of the object of interest. Each reconstructedpoint of the object is the origin of a bundle of lower intensity streaksbut proportional to the intensity of the object in the relevant pointand to the width of the angular pitch for which no measurement isavailable. The streaks, therefore, disappear when the angular pitchtends toward zero, i.e. for a large number of projections covering atleast 180°. When the number of projections is limited by the rate of theimaging apparatus or does not cover 180°, because certain angulationsare not accessible, the image is altered by sub-sampling streaks.

An problem is that the object to be reconstructed may include strongcontrast differences. Thus, the streaks issued from more intensestructures may strongly degrade the less intense structures or the lowercontrast differences.

This phenomenon is all the more significant in the medical field whenthe imaged objects are organs crossed by a contrast product. This isalso the case when the imaged object is a breast in whichmicrocalcifications are found.

BRIEF SUMMARY OF THE INVENTION

With the embodiments of the invention it is possible to reconstruct anobject by tomography with a small number of projections, notably whenthe object to be reconstructed includes significant contrastdifferences.

According to an embodiment of the present invention a method forprocessing a sequence of a plurality of 1D or 2D projection images of anobject of interest is provided. The projection images of the object ofinterest are acquired by a medical imaging system comprising a source ofrays, the source being configured to move around the object in order toacquire the plurality of 1D or 2D projection images of the object ofinterest according to a plurality of angulations, the number of 1D or 2Dprojections and/or the angular coverage leading to the occurrence ofspecific sub-sampling artefacts. The method, being recursive, comprisesdefining, a priori, a sparse image and a series of models for breakingdown the object of interest as a sum of a sparse component and of acomplementary non-sparse component; initializing a sparse 2D or 3D imagedepending on the sparse image defined a priori and initializing theseries of models for breaking down the object of interest;reconstructing a 2D or 3D image of the sparse component of thedecomposition model of the object of interest from acquired 1D or 2Dprojection images and from the initialized sparse 2D or 3D image; andupdating the sparse 2D or 3D image as being equal to the reconstructionof the 2D or 3D image of the sparse component and updating thedecomposition model of the object of interest into a new sparsecomponent and a new complementary non-sparse component, and returning toreconstruction of the 2D or 3D image of the sparse component so that,during the iterations, the reconstruction of the 2D or 3D image of thesparse component gradually reintroduces the complementary component intothe sparse 2D or 3D image, in order to obtain a complete 2D or 3D imageof the non-sparse object of interest.

According to another embodiment of the present invention, a medicalimaging system is provided. The medical imaging system comprises anacquisition unit configured to acquire a plurality of 1D/2D projectionimages of an object of interest, the acquisition unit comprising asource of radiation and a sensor,; and a processing unit configured to:define, a priori, a sparse image and a series of models for breakingdown the object of interest as a sum of a sparse component and of acomplementary non-sparse component; initialize a sparse 2D or 3D imagedepending on the sparse image defined a priori and initializing theseries of models for breaking down the object of interest; reconstruct a2D or 3D image of the sparse component of the decomposition model of theobject of interest from acquired 1D or 2D projection images and from theinitialized sparse 2D or 3D image; and update the sparse 2D or 3D imageas being equal to the reconstruction of the 2D or 3D image of the sparsecomponent and updating the decomposition model of the object of interestinto a new sparse component and a new complementary non-sparsecomponent, and returning to reconstruction of the 2D or 3D image of thesparse component so that, during the iterations, the reconstruction ofthe 2D or 3D image of the sparse component gradually reintroduces thecomplementary component into the sparse 2D or 3D image, in order toobtain a complete 2D or 3D image of the non-sparse object of interest.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Other characteristics and advantages of embodiments of the inventionwill become further apparent from the description which follows, whichis purely illustrative and non-limiting and should be read withreference to the appended drawings, wherein:

FIG. 1 illustrates a medical imaging system according to an embodimentof the invention;

FIG. 2 illustrates a medical imaging system according to an embodimentof the invention;

FIG. 3 illustrates an image processing method according to an embodimentof the invention; and

FIG. 4 illustrates steps of the image processing method according to anembodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

In FIG. 1, a medical imaging system for acquiring 2D projection imagesis schematically illustrated, for reconstructing a 3D image of an organ.Such a system is notably used for detecting and characterizing stenosesin vessels.

The medical imaging system 100 comprises a support 1, intended toreceive a patient 12 to be examined, a source 11 intended to emit a beam10 of X-rays, a detector 13 positioned facing the source 11, andconfigured for detecting the X-rays emitted by the source 11, a controlunit 6, a storage unit 7, and a display unit 8.

Ionizing radiations other than X-rays may be contemplated: notably gammarays. Thus, the tomographic devices used in nuclear medicine (singlephoton emission and transmission tomography and positron emissiontomography) are compliant with embodiments of the invention.

The X-ray source 11 and the detector 13 are, for example, connected bymeans of a arm 15.

The detector 13 may be a semiconducting image sensor for example,comprising a cesium iodide phosphor (scintillator) on atransistor/photodiode array in amorphous silicon. Other adequatedetectors are: a CCD sensor, a direct digital detector which directlyconverts X-rays into digital signals. The detector 13 illustrated inFIG. 1 is planar and defines a planar image surface, other geometriesmay of course be suitable.

The control unit 6 allows the acquisition to be controlled by settingseveral parameters, such as the radiation dose, to be emitted by theX-ray source and the positioning of the source 11 and of the detector13. It is connected to the arm 15 through a wire or wireless connection.

The control unit 6 may comprise a reading device (not shown) for examplea diskette reader, a CDROM, DVDROM reader or connection ports, in orderto read the instructions of the processing method from a medium ofinstructions (not shown), such as a diskette, a CDROM, DVDROM, or USBkey or, more generally, from any removable memory medium, or further viaa network connection.

The storage unit 7 is connected to the control unit 6, for recording theparameters and the acquired images. Provision may be made for locatingthe storage unit 7 inside or outside the control unit 6. The storageunit 7 may be formed by a hard disk or SSD, or any other removable andrewritable storage means (USB keys, memory cards etc.). The storage unit7 may be a ROM/RAM memory of the control unit 6, a USB key, a memorycard, a memory of a central server.

The display unit 8 is connected to the control unit 6, for displayingthe acquired images and/or information on the control parameters of theacquisition. The display unit 8 may for example be a computer screen, amonitor, a flatscreen, a plasma screen or any other type of display unitof a known type. Such a display unit 8 allows the practitioner tomonitor reconstruction and/or display of the acquired 2D images.

The medical imaging system 100 is coupled with a processing system 200.The processing system 200 comprises a computation unit 9 and a storageunit 10. The processing system 200 receives the acquired images storedin the storage unit 4 of the medical imaging system 100, from which itcarries out a certain number of processing operations (see hereafter)for example, a reconstruction of a 3D image from 2D images.

The transmission of the data from the storage unit 4 of the medicalimaging system 100 to the computation unit 9 of the processing system200 may be accomplished through an internal or external computer networkor with any adequate physical memory medium such as diskettes, CDROMs,DVDROMs, external hard disk, USB key, SD card, etc. The computation unit9 is for example, computer(s), microcontroller(s), microcomputer(s),programmable automaton or automata, application-specific integratedcircuits, other programmable circuits, or other devices which include acomputer, such as a workstation.

Alternatively, the computation unit 9 may comprise a reading device (notshown), for example, a diskette reader, a CDROM or DVDROM reader orconnection ports for reading the instructions of the processing methodfrom an instruction medium (not shown), such as a diskette, a CDROM, aDVDROM or a USB key, or more generally from any removable memory medium,or further via a network connection.

Further, the processing system 200 comprises a storage unit 14 forstoring data generated by the computation unit 9. The computation unit 9may be connected to the display unit 8 (as in FIG. 1) or else to anotherdisplay unit (not shown).

The image processing method is for example, implemented in theprocessing unit 200 of the medical imaging system illustrated in FIG. 1.The image processing method allows reconstruction of a 3D image of anobject of interest f from acquired 2D projection images p of the objectof interest, in particular in the case when a contrast product has beeninjected into the object of interest.

A plurality of the 2D projection images obtained by means of the medicalimaging system, the source of which moves along a trajectory around theobject (commonly a rotation, also called spin), are therefore available.

The 2D projection images p are for example, acquired and recoveredbeforehand from the storage unit 14 of the processing unit 200 of themedical imaging system 100 and the processing of the 2D projectionimages is applied in the computer 9 of the processing unit 200 of themedical imaging system.

The 2D projection images p are such that Rf=p, wherein R is theprojection operator which models the finished sampling carried out bythe medical imaging system during the acquisition.

The reconstructed 3D images are affected by striations due tosub-sampling of the object of interest. It is known that sub-samplingmay be compensated by a mathematical a priori according to which theobject of interest is sparse; i.e. compressible. In the vascular case,these are the vessels of the object of interest. These vessels arerevealed by injecting a contrast product. The passage time of thiscontrast product does not allow acquisition of a sufficient number ofprojections and in certain cases, even if the acquisition covers 180°,the angular coverage for which the contrast product is present is lessthan 180° , because of poor synchronization between the injection of theproduct, its diffusion and the acquisition of the images.

Typically, the distribution of the vessels injected into an organ has asupport limited to a rather low fraction of the 3D image of the organ.It is therefore sparse. On the other hand, the sparsity assumptioncannot be as strong for the remainder of the contents of the image(bones, soft tissues).

The acquisition therefore has to be accomplished by subtraction: twoidentical spins are acquired, one without contrast product injection,the other one with injection, so that the subtraction of both spins onlycorresponds to the vessels which are sparse. The integration of theacquired 2D projection images and of the compressibility assumption isaccomplished by the definition of the functional:

J(g,λ)=λS(g)+Q(g),

wherein Q is a quadratic tomographic reconstruction criterion, as forexample, as described or referenced in documents [Riddell C, Savi A,Gilardi M C, Fazio F, “Frequency weighted least squares reconstructionof truncated transmission SPECT data.” IEEE Trans. Nucl. Sci.43(4):2292-8] and [Thibault J B, Sauer K D, Bouman C A, Hsieh J, “Athree-dimensional statistical approach to improved image quality formulti-slice helical CT” Med. Phys.3(11):4526-44]. And wherein S is asparsity constraint defined by:

S(g)=∥Φ_(xyz) g∥₁

wherein ∥ ∥₁ symbolizes the so-called L₁ norm and Φ_(xyz) is a transformallowing spatial compression of the 3D image g (wavelet transform,gradient, identity . . . ). More generally S may be the weighted sum ofseveral of these spatial transforms and may combine other a priori knownpieces of information on the image, such as the positivity of the X-rayattenuation coefficients. The scalar λ is a weight, which defines thesparsity constraint force, in other words, the degree of compressibilityof the sought solution.

As known for minimizing the functional J(g,λ) with respect to g forfixed λ and obtaining an estimation of f, solution of the perfectlysampled tomographic reconstruction problem, a convex optimizationiterative algorithm may be used for minimization of J(g,λ), for exampleone of those described or referenced in [Afonso M V, Bioucas-Dias J M,Figueirido M A, “Fast image recovery using variable splitting andconstrained optimization.” IEEE Trans. Image Process. (9):2345-56] and[Beck A, Teboulle M. “Fast gradient-based algorithms for constrainedtotal variation image denoising and deblurring problems.” IEEE Trans.Image Process. P. 18(11):2419-34].

The iteration allowing minimization of J(g,λ) with respect to g forfixed λ is noted as A_(k) and the 3D image resulting from theapplication of κ iteration(s) of the algorithm initiated from the 3Dimage g is noted as A_(λ) ^(κ)[g]. Indeed, except in the perfectlysampled case, it will be noted that these algorithms produce differentimages depending on the image g, from which the iterative optimizationmethod is initiated.

For example, it is recalled that the minimization of J(g,λ) is obtainedby:

g ^((κ+1)) =A _(λ) [g ^(κ)]=prox_(ρλ) S(g ^(κ) −ρ∇Q(g ^(κ))),

with ρ a scalar assumed to be sufficiently small in order to guaranteeconvergence of A_(λ) ^(κ), ∇Q(g) being the gradient of Q at g, and

${{prox}_{\gamma}{S(g)}} = {\arg_{h}\min \{ {{\frac{1}{2}{{g - h}}^{2}} + {\gamma \; {S(h)}}} \}}$

is the application of the proximal operator of S to g for γ=ρλ a scalar.

Applying a similar step for A_(λ) may be contemplated by calculatingA_(λ)(g^((κ))), not only from the iteration g^((κ)) but also from theiteration g^((κ-1)) or else further from all of the previous iterations.

By using either one of these algorithms, the sparsity constraint isapplied on the totality of the object of interest.

In a novel way, these same algorithms are considered to be applicable inthe case when the object of interest does not meet the sparsityconstraint (impossible subtraction in the vascular case); an approximate(in particular biased) reconstruction of the sparse portions is thenobtained at the cost of an extreme simplification or of a total loss ofthe other structures.

Such a reconstruction will be described as “selective” subsequently inthis document since it selectively gives access to one or several sparsestructures of the object of interest independently of the other ones.This selection is modulated by the intensity of the parameter λ. For ahigh value of λ, a very restricted set of structures is selected, for avery low or zero value, the reconstruction differs little or does notdiffer from a standard quadratic reconstruction, including all thestructures, even those which are not sparse, and all the sub-samplingartefacts.

The originality of the embodiments the invention comes from the factthat only isolated structures of the object of interest are consideredas sparse. Thus, always valid assumptions are made that a sparse imageof the object of interest is known a priori (knowledge which may bezero), an assumption noted as H1, and that the object may be modelled apriori in a first sparse component, including the a priori known portionand in a second complementary and non-sparse component, called a“background” assumption noted as H2.

A selective reconstruction of the sparse portion is carried out by oneof the aforementioned algorithms, initiated from the a priori knownsparse image. This principle is however generalized by proceedingrecursively per level: at each level, the sparse image is redefined asbeing equal to the sparse portion calculated at the previous level(assumption H1), and then the a priori model of the object is redefinedby “enlarging” the sparse component (in other words, the intensity ofthe parameter λ is reduced), assumption H2.

The recursion is, for example, initiated by a zero sparse 3D image (zeroassumption H1) and ends for zero intensity k (assumption H2 where theso-called sparse component includes the whole object, although it is notsparse, and the complementary background component is zero).

The benefit of the method is to suppress the striations associated withthe sparse component by the sparsity constraint, before reconstructingthe background and avoiding degradation of the background by thestriations. The striations, vessels in the vascular case,microcalcifications in the case of the breast tomosynthesis, are reducedor suppressed from the background. The recursion is therefore defined asa series of a priori models, defining at each level a sparse componentand an complementary non-sparse component, which is simply expressed asa decreasing series of compressibility degrees Λ={λ₁, . . . , λ_(Ξ)}such that λ₁> . . . >λ_(Ξ)≧0, for which, from the a priori sparse imageg₀, possibly zero, an estimation g*(Λ,g₀) of a non-sparse solution f ofthe perfectly sampled tomographic reconstruction problem is determinedaccording to:

$\quad\{ \begin{matrix}{g_{0},{\Lambda = \{ {\lambda_{1},\ldots \mspace{14mu},\lambda_{\Xi}} \}}} \\{{g( \lambda_{1} )} = {A_{\lambda_{\xi}}^{\kappa}\lbrack g_{0} \rbrack}} \\{{g( \lambda_{\xi} )} = {{{A_{\lambda_{\xi}}^{\kappa}\lbrack {g( \lambda_{\xi - 1} )} \rbrack}\mspace{31mu} \xi} \in \{ {2,\ldots \mspace{14mu},\Xi} \}}} \\{{g^{*}( {g_{0},\Lambda} )} = {g( \lambda_{\Xi} )}}\end{matrix} $

In order to explain the course of the method for obtaining g*(A,g₀),which is the complete reconstruction off the a priori image g₀ and Λ theseries of the models for breaking down the object, which is expressed asa sequence of compressibility degrees, are set (E₁). The sparse 3D imageg_(p)=g₀ and the model for breaking down the object are initiated (E₂),by setting λ=λ_(ξ). The selective reconstruction is calculated (E₃)g(λ)=A_(λ) _(ξ) ^(κ)[g_(p)], which is the sequence of κ iterations,which minimizes the functional J(g,λ) with respect to g, for λ=λ₁ bystarting with the sparse image g_(p). Next, iteratively, at iteration ξ∈ {2, . . . , Ξ}, the sparse image g_(p)=g(λ_(ξ−1)) and the parameter ofthe decomposition model λ=λ_(ξ) are updated (E₄) in order to return tostep E₃. Thus, for τ=Ξ, the complete reconstruction g*(Λ,g₀)=g(λ_(Ξ)) ofthe non-sparse object is obtained (E₅).

The method according to embodiments of the invention therefore consistsof applying a succession of iterative 3D reconstructions which are lessand less selective, from the set of acquired 2D projection images, butinitiated by a sparse 3D image containing more and more structures,possibly reconstructed without any sub-sampling artefacts, so that theeliminated structure(s) are gradually reintroduced into the selective 3Dreconstruction image in order to obtain a complete 3D image of theobject of interest, estimated from the perfectly sampled object ofinterest.

It will be noted that the method, advantageously, neither makes anyassumption on the acquired 2D projections nor requires anypre-processing specific to the method for these images. Onlypre-processing operations which are customary for any tomographicreconstruction method for X-ray images are required.

Preferably, the following operators and constraints are used:

∇Q(g)={tilde over (R)}(Rg−p)

wherein {tilde over (R)} is an operator which models the filteredback-projection; the sparsity constraint combines Φ_(xyz)(g)=g with apositivity constraint so that the proximal operator prox_(γ)S(g) is athreshold operator γ for soft subtraction from the background of a 3Dimage, noted as B_(γ)(g). This operator consists of:

setting to zero the pixels of the image for which the value is below thethreshold,

subtracting γ from the pixels for which the value is above the thresholdγ.

More generally, any segmentation operator by thresholding of a 3D imagemay be used, which:

sets to zero the pixels of the image having an intensity below a setthreshold;

and/or reduces the intensity of pixels of the image by the value of athreshold;

and/or sets to zero, pixels of the image located outside a set area.

According to a particular embodiment, the processing method according tothe invention consists in the following recursion:

$\quad\{ \begin{matrix}{g_{0},\mspace{14mu} {\lambda_{\xi} = {{{{\tau ( {\Xi - \xi} )}/( {\Xi - 1} )}\mspace{31mu} \xi} \in {{\{ {1,\ldots \mspace{14mu},\Xi} \} \mspace{31mu} \rho} > 0}}}} \\ {{g( \lambda_{1} )} = {B_{\rho \; \tau}( {\rho \overset{\sim}{R}p} )}} ) \\{{g( \lambda_{\xi} )} = {B_{{\rho\lambda}_{\xi}}( {{g( \lambda_{\xi - 1} )} - {\rho {\overset{\sim}{R}( {{{Rg}( \lambda_{\xi - 1} )} - p} )}}} )}}\end{matrix} $

wherein τ is a constant defining a pixel level intensity, for example90% of the maximum intensity of the result of the filteredback-projection {tilde over (R)}p.

In this particular embodiment, the first iteration ξ=1 leads to a stepfor filtered back-projection of the acquired 2D projection images. Theresult of this step is subject to a segmentation step by softsubtraction giving an image in which the background has been suppressed,the threshold of the subtraction corresponding to the weight of thegiven constraint.

Here the constraint is a sparsity constraint, which consists ofconsidering that in the image, the structures having an intensity levelabove a threshold τ are sparse, the other ones not being sparse. Thissparsity constraint is released in the following iterations ξ ∈ {2, . .. , Ξ} so as to reintroduce the eliminated areas, the threshold τ beingreplaced with a gradually linearly decreasing threshold during theiterations, i.e. the areas which have an intensity above an increasinglylower threshold are selected at each iteration.

The fact of having selected in a first phase, the images having thestrongest intensities, causes reconstruction of these areas without theassociated striations by the sparsity constraint, which then allows thereintroduction of the previously eliminated areas without reintroducingthe striations associated with the strongest intensities.

Alternatively, the decrease of the threshold may follow a decreasingpiecewise constant function.

The applications described above within the scope of injecting acontrast product into vessels are transposed without any modificationinto the case of breast tomosynthesis. Microcalcifications are sparsestructures of very high intensity which may generate striationsdegrading the non-sparse structures of the background consisting ofglandular and adipous tissues.

On the other hand, in the particular case where a lack of injection ofthe contrast product leads to having a set of components of the 2Dprojection images, such that some of them are without any contrastproduct, the complementary steps are introduced, consisting of:

-   AA) partitioning (E₀) of the components of the 2D projection images    acquired in a subset of components without any contrast product,    steps E₁ to E₅ being applied in order to process the subset of    components with a contrast product and to obtain a complete 3D image    of the object with a contrast product;-   BB) reconstructing (E₆) by filtered back-projection the subset of    components without any contrast products and obtaining a 3D image of    the object of interest without any contrast product;-   CC) determining (E₇) a 3D image, a weighted average of the 2D/3D    image of the object with a contrast product obtained in step AA)    (E₀-E₅) and of the 3D image of the object without any contrast    product obtained in step BB) (E₆);-   DD) iteratively reconstructing (E₈) the subset of components with a    contrast product from the 3D composite image obtained in step CC)    (E₇) so as to obtain an improved complete 3D image of the object    with a contrast product.

The description which follows is made in the case of 3D reconstruction,i.e. from 2D projections. Of course, this description extends to thecase of a 2D reconstruction, i.e. from 1D projections.

The method described above may be implemented as a computer programcomprising machine instructions for applying the method.

1. A method for processing a sequence of a plurality of 1D or 2Dprojection images of an object of interest, wherein the projectionimages of the object of interest are acquired by a medical imagingsystem comprising a source of rays, the source being configured to movearound the object in order to acquire the plurality of 1D or 2Dprojection images of the object of interest according to a plurality ofangulations, the number of 1D or 2D projections and/or the angularcoverage leading to the occurrence of specific sub-sampling artefacts,the method being recursive and comprising: defining, a priori, a sparseimage and a series of models for breaking down the object of interest asa sum of a sparse component and of a complementary non-sparse component;initializing a sparse 2D or 3D image depending on the sparse imagedefined a priori and initializing the series of models for breaking downthe object of interest; reconstructing a 2D or 3D image of the sparsecomponent of the decomposition model of the object of interest fromacquired 1D or 2D projection images and from the initialized sparse 2Dor 3D image; and updating the sparse 2D or 3D image as being equal tothe reconstruction of the 2D or 3D image of the sparse component andupdating the decomposition model of the object of interest into a newsparse component and a new complementary non-sparse component, andreturning to reconstruction of the 2D or 3D image of the sparsecomponent so that, during the iterations, the reconstruction of the 2Dor 3D image of the sparse component gradually reintroduces thecomplementary component into the sparse 2D or 3D image, in order toobtain a complete 2D or 3D image of the non-sparse object of interest.2. The method according to claim 1, wherein the reconstruction of the 2Dor 3D image of the sparse component comprises applying to the acquired1D or 2D projection images a reconstruction assuming that the object ofinterest is sparse.
 3. The method according to claim 1, wherein defininga sparse image and a series of models for breaking down the object ofinterest comprises breaking down the object of interest according to theintensities of pixels relatively to a threshold such that if theintensity of the pixel is above the threshold, the pixel belongs to thesparse component, and if the intensity of the pixel is below thethreshold, the pixel belongs to the complementary component.
 4. Themethod according to claim 1, wherein defining a sparse image and aseries of models for breaking down the object of interest comprisesbreaking down the object of interest according to a localization of thepixel in the 2D or 3D image depending on whether its index belongs to aset of indexes of the sparse component or to a set of indexes of thecomplementary component.
 5. The method according to claim 1, whereinreconstructing the 2D or 3D image of the sparse component comprises asegmentation, the segmentation comprising at least one of: setting tozero the pixels of the image with an intensity less than a giventhreshold; reducing the intensities of the pixels of the image by thevalue of a threshold; setting to zero the pixels of the image for whichthe indexes belong to a set of given indexes.
 6. The method according toclaim 1, wherein reconstructing the 2D or 3D image of the sparsecomponent comprises filtered back-projection.
 7. The method according toclaim 6, comprising the following recursion:$\quad\{ \begin{matrix}{g_{0},\mspace{14mu} {\lambda_{\xi} = {{{{\tau ( {\Xi - \xi} )}/( {\Xi - 1} )}\mspace{31mu} \xi} \in {{\{ {1,\ldots \mspace{14mu},\Xi} \} \mspace{31mu} \rho} > 0}}}} \\{{g( \lambda_{1} )} = {B_{\rho \; \tau}( {g_{0} - {\rho {\overset{\sim}{R}( {{Rg}_{0} - p} )}}} )}} \\{{g( \lambda_{\xi} )} = {{{B_{{\rho\lambda}_{\xi}}( {{g( \lambda_{\xi - 1} )} - {\rho {\overset{\sim}{R}( {{{Rg}( \lambda_{\xi - 1} )} - p} )}}} )}\mspace{31mu} \xi} \in \{ {2,\ldots \mspace{14mu},\Xi} \}}}\end{matrix} $ wherein g₀ is an image of the object of interestknown a priori, λ_(ξ) belongs to a sequence which is set a priori, of Ξthresholds linearly decreasing from τ to 0, p is the vector of theacquired 1D or 2D projections, R is a projection operator which modelsthe acquisition of the projection images, {tilde over (R)} is anoperator modelling the filtered back-projection, ρ is a scalarguaranteeing conversion of the method and B_(γ) is a segmentationthresholding operator with a threshold γ.
 8. The method according toclaim 7, wherein λ_(ξ) belongs to a series of Ξ thresholds decreasingfrom τ to 0 according to a piecewise constant function so that eachthreshold remains unchanged for a predetermined number of iterations. 9.The method according to claim 1, wherein the a priori image of theobject of interest is zero.
 10. The method according to claim 1, whereinthe acquired 1D or 2D projection images comprise a subset of componentswithout any contrast product and a subset of components with a contrastproduct, wherein defining a sparse image and a series of models forbreaking down the object of interest, initializing a sparse 2D or 3Dimage, reconstructing the 2D or 3D image of the sparse component andupdating the sparse 2D or 3D image are applied for processing the subsetof components with a contrast product; and wherein the method furthercomprises: reconstructing by filtered back-projection the subset ofcomponents without any contrast product and obtaining a 2D or 3D imageof the object of interest without any contrast product; determining a 2Dor 3D image, a weighted average of the 2D or 3D image of the object witha contrast product and of the 2D or 3D image of the object without anycontrast product obtained by reconstructing by filtered back-projectionthe subset of components without any contrast product; iterativelyreconstructing the subset of components with a contrast product from the2D or 3D composite image obtained by determining a 2D or 3D image so asto obtain an improved complete 2D or 3D image of the object with acontrast product.
 11. A medical imaging system comprising: anacquisition unit configured to acquire a plurality of 1D or 2Dprojection images of an object of interest, the acquisition unitcomprising a source of radiation and a sensor; and a processing unitconfigured to: define, a priori, a sparse image and a series of modelsfor breaking down the object of interest as a sum of a sparse componentand of a complementary non-sparse component; initialize a sparse 2D or3D image depending on the sparse image defined a priori and initializingthe series of models for breaking down the object of interest;reconstruct a 2D or 3D image of the sparse component of thedecomposition model of the object of interest from acquired 1D or 2Dprojection images and from the initialized sparse 2D or 3D image; andupdate the sparse 2D or 3D image as being equal to the reconstruction ofthe 2D or 3D image of the sparse component and updating thedecomposition model of the object of interest into a new sparsecomponent and a new complementary non-sparse component, and returning toreconstruction of the 2D or 3D image of the sparse component so that,during the iterations, the reconstruction of the 2D or 3D image of thesparse component gradually reintroduces the complementary component intothe sparse 2D or 3D image, in order to obtain a complete 2D or 3D imageof the non-sparse object of interest.